Iterative Methods for Toeplitz Systems Numerical Mathematics and Scientific Computation Series

Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed. The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyse new methods for other types of problems and applications.

Notations and definitions. Iterative methods, Theory. Toeplitz systems. Circulant preconditioners. Non-circulant type preconditioners. Ill-conditioned Toeplitz systems. Structured systems, Applications. Applications to ordinary and partial differential equations. Applications to queuing networks. Applications to signal processing. Applications to image processing. Applications to integral equations.

Researchers and graduate students working in engineering and mathematics.

Michael K. Ng is an Associate Professor in the Department of Mathematics and also Adjunct Research Fellow in the E-Business Technology Institute at The University of Hong Kong.